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One of the most important tasks in the food industry is the search for alternative biochemical markers of radiation treatment in dietary, chilled meat products such as chicken and turkey. Major organic volatile chemicals found in meat products can be precisely identified using gas chromatography coupled with mass spectrometry. In the response to the needs of the food industry, our research team conducted a series of experiments involving the irradiation of chilled poultry meat using an electron accelerator. The experiments showed that the concentration of pure volatile organic compounds in saline solution dropped exponentially with an increase in the irradiation dose, which proves that these chemicals decomposed when exposed to ionizing radiation. However, when turkey meat was exposed to an electron beam with doses up to 1 kGy, the concentration of alcohols, aldehydes, and ketones peaked, only to decrease with an increase in the irradiation dose up to 2 kGy, and then went up slightly when the irradiation dose was within the range from 2 kGy to 10 kGy. To determine the reason behind the nonlinear dependencies of organic compound concentrations in turkey meat on the irradiation dose, we developed a mathematical model that acknowledges the presence of two opposing processes, those of decomposition and accumulation of organic compounds as a result of the decomposition of other compounds that can be found in turkey meat.